Stabilization of Direct Learning Algorithm for Wideband Signals

ABSTRACT

The present invention addresses method, apparatus and computer program product for stabilization of the direct learning algorithm for wideband signals. Thereby, a signal to be amplified is input to a pre-distorter provided for compensating for non-linearity of the power amplifier, and the pre-distorted output signal from the pre-distorter is forwarded to the power amplifier. Parameters of the pre-distorter are adapted based on an error between the linearized signal output from the power amplifier and the signal to be amplified using an adaptive direct learning algorithm, and the linear system of equations formed by the direct learning algorithm are solved using a conjugate gradient algorithm, wherein, once per direct learning algorithm adaptation, at least one of the initial residual and the initial direction of the conjugate gradient algorithm are set based on the result of the previous adaptation.

FIELD OF THE INVENTION

The present invention generally relates to wireless mobile communicationsystem, and more specifically relates to an apparatus and method forstabilization of the direct learning algorithm for wideband signals.

BACKGROUND

In wireless mobile communication a wideband mobile communication systemusing complex modulation techniques is known, wherein such technologiesoften require linear power amplifiers PA for its radio frequency RFtransmissions. However, in general, low power consumption is aspired formobile systems. Therefore, a power amplifier may be operated atcompressed regions.

In general, a power amplifier and an associated low power analogtransmitter in radio devices behave non-linearly when operated atcompressed regions. Since non-linearity may cause severe problems inregard of control of the system, it is expedient to eliminate or atleast abate the non-linearity thereof. One possible approach that solvesthe non-linearity issue is to conduct a considerable back off, so thatthe operation region becomes linear. However, this is very inefficientand does not yield desired power savings.

Further, digital baseband pre-distortion has been recognized as a costeffective technique for linearizing power amplifiers PA. According tothis technique, the PA input signal is distorted by a pre-distortionmeans whose characteristics are basically the inverse of those of theamplifier. That is, a Digital Pre-Distortion DPD algorithm applyingorthogonal polynomials used for control in radio devices that allows theRF signal to operate in the compression region is known. Operating incompressive regions enables power savings due to increased efficiency.However, operating in such regions will also increase the intermodulation IM products. However, Increase of IM products in generalviolates the 3GPP specifications.

Thus, the primary role of the DPD algorithm is to reduce the IMproducts, so that the radio device can operate efficiently in compliancewith the 3GPP specifications.

In general, there are two broad categories of DPD algorithms:

-   -   a) DPD algorithms that compute the correct PA model or the        inversion model in a single try;    -   b) DPD algorithms that compute the correct PA model or the        inversion model adaptively using many tries.

Both categories yield the correct answer. Category a) can be used toimplement a ‘Direct-’ as well as an ‘Indirect Learning Algorithm’. In adirect learning algorithm DLA, the non-linearity is modeled from inputto output, i.e. model equations from input variables describe theoutput. In an Indirect Learning Algorithm ILA, the non-linearity ismodeled from the output to input, i.e. equations that consist of theoutput signal describe the input. Typically, in an ILA method, theinverse non-linear model is computed in a single try. Hence, no extraeffort is required to compute the inverse model.

With the direct learning algorithm the non-linear model is obtainedrather than the inverse model. Hence, an iterative process is normallypursued to obtain the inverse. With category a) algorithms, thisinversion process is fixed to a pre-determined value (i.e. 2, 3, . . . ,5 etc). Examples are the fixed point algorithms with N1 iterations orNewton Method with N2 iterations. N1 and N2 are selected based on therequired convergence accuracy of the inverse model. Another factor thatlimits N1 and N2 are hardware limitations.

On the other hand, DLA or ILA algorithms can be implemented adaptivelyas well. Due to its simplicity, the adaptive implementation of ILA israrely pursued. However, it is very common to have DLA implemented in anadaptive manner via a known inversion algorithm listed above.

Adaptive implementation of fixed point method or Newton method can beparticularly advantageous if newer updates are always better than theprevious update. In this case, N1 and N2 can be infinite (practicallyvery large). Since DLA accuracy improves with larger N1 and N2, the bestcorrection results for a DPD system may be achieved.

In general, DLA algorithms that are adaptively implemented specify anerror bound. Hence, if this error bound is achieved after N3 adaptations(i.e. error is lower than the bound), the inverse model is assumed to beaccurate. The algorithm will stop at N3. If for some reason the staticconditions cannot be maintained due to slow perturbation of thenon-linear system, the adaptive algorithm needs to be re-started fromthe initial conditions. This is normally called the restart of thealgorithm.

However, the above ‘adapt and stop mechanism’ is only suited for staticconditions where the non-linear system doesn't change frequently. In awireless environment where dynamic data traffic models exist, the poweramplifier tends to change continuously. Further, dynamic trafficconditions cause the power amplifier temperature to change. In addition,the dynamic traffic can change the gain of the power amplifier as well.Another factor that changes the power amplifiers is aging due tolifetime.

While a periodic restart of the algorithm would solve the dynamictraffic cases, the time to achieve the error bound is an importantfactor in commercial radios. Until the final error bound is achieved, itis safe to assume that inter-modulation (IM) products will not achievethe 3GPP specifications.

Hence, in a wireless environment, the continuous adaptation maypreferably take place in anticipation of PA change. However, thecontinuous adaptation can bring instability due to numerical erroraccumulation (e.g. floating point errors). This is because whenadaptations tend to be very large, even a small numerical error per stepcan cause a huge accumulation of noise.

In some instances (more likely with narrow band signals) instabilityoccurs after 1000s of adaptations. However, with wideband signals, thisinstability can occur in less than 100 adaptations. If this instabilityis not checked, the adaptive DLA algorithm will diverge causing intermodulation products to rise with time.

SUMMARY OF THE INVENTION

In order to overcome the drawbacks of the prior art, it is an objectunderlying the present invention to provide an improved wireless mobilecommunication system, and more specifically to provide an improvedapparatus, method and computer program product for stabilization of thedirect learning algorithm for wideband signals.

According to a first aspect of the present invention, there is provideda method for controlling a power amplifier operating in a non-linearstate, comprising inputting a signal to be amplified to a pre-distorterprovided for compensating for non-linearity of the power amplifier,forwarding the pre-distorted output signal from the pre-distorter to thepower amplifier, adapting parameters of the pre-distorter based on anerror between the linearized signal output from the power amplifier andthe signal to be amplified using an adaptive direct learning algorithm,and solving the linear system of equations formed by the direct learningalgorithm using a conjugate gradient algorithm, wherein, once per directlearning algorithm adaptation, at least one of the initial residual andthe initial direction of the conjugate gradient algorithm are set basedon the result of the previous adaptation.

According to a second aspect of the present invention, there is providedAn apparatus for controlling a power amplifier, comprising apre-distorter, at least one processor, and at least one memory forstoring instructions to be executed by the processor, wherein the atleast one memory and the instructions are configured to, with the atleast one processor, cause the apparatus at least to perform inputting asignal to be amplified to a pre-distorter provided for compensating fornon-linearity of the power amplifier; forwarding the pre-distortedoutput signal from the pre-distorter to the power amplifier, adaptingparameters of the pre-distorter based on an error between the linearizedsignal output from the power amplifier and the signal to be amplifiedusing an adaptive direct learning algorithm, and solving the linearsystem of equations formed by the direct learning algorithm using aconjugate gradient algorithm, wherein, once per direct learningalgorithm adaptation, at least one of the initial residual and theinitial direction of the conjugate gradient algorithm are set based onthe result of the previous adaptation.

According to a third aspect of the present invention, there is provideda computer program product comprising computer-executable componentswhich, when the program is run, are configured to carry out the methodaccording to the first aspect.

Advantageous further developments or modifications of the aforementionedexemplary aspects of the present invention are set out in the dependentclaims.

According to certain embodiments of the invention, the initial residualand/or the initial direction of the conjugate gradient algorithm is/areset at the beginning of the adaptation.

According to certain embodiments of the invention, the initial residualand/or the initial direction of the conjugate gradient algorithm is/areset so as to fulfill the following equations:

r _(init) =b−A*x _(n−1)

d _(init) =r _(init)

-   -   wherein r_(init) is the initial residual vector, d_(init) is the        initial direction vector, b is the cross-correlated vector of        the error, A is the autocorrelation matrix, and x_(n−1) is the        solution vector at the (n−1)^(th) direct learning algorithm        adaptation.

According to certain embodiments of the invention, loops of theconjugant gradient algorithm are iterated until reaching a preset numberof loops. Thereby, the preset number of loops is far less than what isrequired by the standard conjugate gradient algorithm (i.e. 4-32 loopsvs. 1000s for adaptation).

According to certain embodiments of the invention, the initial residualand/or the initial direction of the conjugate gradient algorithm is/arecomputed based on the partially converged solution of the previousadaptation.

According to certain embodiments of the invention, an error scalingfactor is introduced In the adaptive direct learning algorithm, so as tofulfill the following equation:

y(n)=x(n)−μ*e(n)

wherein y is the pre-distorted signal vector, x is a vector of thesignal to be amplified, e is the error vector, μ is the error scalingfactor, and indicates the adaptation number. Thereby, the error scalingfactor may be set to a value smaller than 1.0, preferably to μ=(0.1,0.2, 0.25, 0.5, . . . ).

BRIEF DESCRIPTION OF DRAWINGS

For a more complete understanding of example embodiments of the presentinvention, reference is now made to the following descriptions taken Inconnection with the accompanying drawings In which:

FIG. 1 schematically illustrates a direct learning architecture forperforming an adaptive direct learning algorithm according to certainembodiments of the present invention;

FIG. 2 shows a principle configuration of an example for a methodaccording to certain embodiments of the present invention; and

FIG. 3 shows a principle flowchart of an example for an apparatusaccording to certain embodiments of the present invention.

DESCRIPTION OF EXEMPLARY EMBODIMENTS

Exemplary aspects of the present invention will be described hereinbelow. More specifically, exemplary aspects of the present invention aredescribed hereinafter with reference to particular non-limiting examplesand to what are presently considered to be conceivable embodiments ofthe present invention. A person skilled in the art will appreciate thatthe invention is by no means limited to these examples, and may be morebroadly applied.

It is to be noted that the following description of the presentinvention and its embodiments mainly refers to specifications being usedas non-limiting examples for certain exemplary network configurationsand deployments. Namely, the present invention and its embodiments aremainly described in relation to 3GPP specifications being used asnon-limiting examples for certain exemplary network configurations anddeployments. As such, the description of exemplary embodiments givenherein specifically refers to terminology which is directly relatedthereto. Such terminology is only used in the context of the presentednon-limiting examples, and does naturally not limit the invention in anyway. Rather, any other network configuration or system deployment, etc.may also be utilized as long as compliant with the features describedherein.

Hereinafter, various embodiments and implementations of the presentinvention and its aspects or embodiments are described using severalalternatives. It is generally noted that, according to certain needs andconstraints, all of the described alternatives may be provided alone orin any conceivable combination (also including combinations ofindividual features of the various alternatives).

In particular, the following examples, versions and embodiments are tobe understood only as illustrative examples. Although the specificationmay refer to “an”, “one”, or “some” example version(s) or exampleembodiment(s) in several locations, this does not necessarily mean thateach such reference is to the same example version(s) or exampleembodiment(s), or that the feature only applies to a single exampleversion or example embodiment. Single features of different exampleembodiments may also be combined to provide other example embodiments.Furthermore, words “comprising” and “including” should be understood asnot limiting the described example embodiments to consist of only thosefeatures that have been mentioned and such example versions and exampleembodiments may also contain also features, structures, units, modulesetc. that have not been specifically mentioned.

FIG. 1 schematically illustrates a direct learning architecture forperforming an adaptive direct learning algorithm according to certainembodiments of the present invention. In particular, supported equationsof the adaptive DLA are shown therein. Nevertheless, it is to be notedthat the formulas supporting FIG. 1 may diverge when the accumulatedfloating point error is significant compared to the inter-modulation(IM) corrections.

As is depicted in FIG. 1, the signal x(n) indicates an un-pre-distortedsignal which is input in a pre-distortion means. An output of thepre-distortion means is labeled with y(n), which indicates apre-distorted signal.

The signal indicated as z(n) is a linearized signal. In the best casethis signal should be as close as possible to x(n). For simplicity gainand phase of the PA are normalized to unity gain and zero phase.

The signal e(n) indicates an error between z(n) and x(n). The ideaaccording to certain embodiments of the present invention is to minimizethis error.

An adaptation X*H=e is performed based on the pre-distorted signal x(n)and the error e(n), and the pre-distortion is adapted according to theadaptation, so as to achieve an accurate signal y(n) which is to beinput in the power amplifier PA.

In the following, equations supporting the traditional DLA are shown:

In order to obtain the error e(n) in adaptive step n, the followingequation (1) applies:

e(n)=z(n)−x(n)  (1)

According to the direct learning algorithm DLA in the ‘A*H=b’ form(system of linear equations), A is the autocorrelation matrix (X^(H) X),and b is the cross correlated vector X^(H)e(n). L1 in the followingequations (2) depicts the order of non-linearity. Thereby, x′ is not avector function.

X=[x′(n)x′(n−1)x′(n−T) . . . x′(n)|x(n)|^(L1) x′(n−1)|x′(n−1)|^(L1)x′(n−T)|x′(n−T)|x′(n−T)|^(L1)

x′(N+n)x′(N+n−1)x′(N+n−T) . . . x′(N+n)|x′(N+n)|^(L1)x′(N+n−1)|x′(N+n−1)|^(L1) x′(N+n−T)|x′(N+n−T)|^(L1)]

H=[h′(n)h′(n−1) . . . h′(n−T)]^(T)

(X ^(H) X)*H=X ^(H) E

E=[e′(n)e′(n+1) . . . e′(n+N)]^(T)

A*H=b form  (2)

Then, generating the pre-distorted signal at adaptive step n is obtainedby the following equation (3):

y(n)=x(n)−e(n)  (3)

wherein e(n)=X*H  (4)

As shown in the equations (1) to (4), when the system is near itsoptimum convergence, z(n) is as close as possible to x(n). Then, theerror e(n) is considerably small. In turn, errors are significantcompared to when e(n) was large at the beginning of the adaptationprocess.

Hence, the continued operation of the same steps at convergence willcause floating point errors to accumulate. These errors will then beabsorbed by the matrix solution to the vector H, where H=[h(n)h(n−1) . .. h(n−T)]^(T). Typical Matrix solutions used in this case are: LUdecomposition, Cholesky decomposition etc. However, this process causesdivergence of the DLA algorithm.

Generally, as indicated above, the basic structure of the DLA algorithmis known. However, according to certain embodiments of the presentinvention a stabilization of the DLA algorithm is provided, so as tostabilize the adaptive DLA algorithm.

According to certain embodiments of the present invention, a measure tocope with DLA instability is the use of conjugate gradient algorithm ina non-standard way.

Generally, the conjugate gradient algorithm is a numerical solution forparticular systems of linear equations, namely those whose matrix issymmetric and positive-definite. The conjugate gradient algorithm ismainly implemented as an iterative algorithm.

However, the standard use of the conjugate gradient algorithm is neithersuitable nor cost effective in terms of computational power. Most radiodevices have limited processing power. Hence, an increase of cost due tothe conjugate gradient requirements is not a viable option.

Non-traditional use of the conjugate gradient algorithm includes the useof significant of reduction in iterative steps used in computation ofA*H=b. The traditional use of the conjugate gradient algorithm requiresnearly 100s (closer to 1000) of iterations to obtain a satisfactorysolution to vector coefficients of H in A*H=b.

The standard conjugate gradient algorithm is briefly depicted below. Inthe standard use of the conjugate gradient method in the adaptive DLA,at the initial step, r_(k) (the residual) and the direction d_(k) areassigned equal to the cross correlation matrix, as shown in equation(5). (k=0 at the initial step).

d _(k) =r _(k) =b  (5)

Then, a loop according to equations (6) to (10) below is performed,until r_(k) is less than the specified error bound a which is defined tobe very small.

Start of Loop

$\begin{matrix}{\alpha_{k} = \frac{r_{k}^{T}r_{k}}{d_{k}^{T}{Ad}_{k}}} & (6)\end{matrix}$

wherein α_(k) is a constant,

x _(k) =x _(k−1)+α_(k) d _(k)  (7)

wherein x_(k) is the current approximation to the vector H in the(A*H=b),

r _(k) =r _(k−1)−α_(k) Ad _(k)  (8)

wherein r_(k) is the new residual,

$\begin{matrix}{\beta_{k} = \frac{r_{k}^{T}r_{k}}{r_{k - 1}^{T}r_{k - 1}}} & (9)\end{matrix}$

wherein β_(k) is a constant,

d _(k) =r _(k)+β_(k) d _(k−1)  (10)

wherein d_(k) is the new direction.

End of Loop

At every DLA adaptation, all of the conjugate gradient steps have to berepeated. This includes the initialization of the residual as well asthe direction. In addition the loop has to be repeated about 1000 times(depends on the size of A in A*H-b, A being the autocorrelation matrix)to bring the residual below ε. Generally, the error bound ε is set to bevery small. Preferably, the error bound is set almost equal to zero fora most satisfactory solution.

It becomes apparent that the standard conjugate gradient steps cannot beadopted in this form for a commercial product. The idea that makes theconjugate algorithm feasible for a commercial product is describedbelow.

FIG. 2 shows a principle flowchart of an example for a method accordingto certain embodiments of the present invention.

In Step S21, a signal to be amplified is input to a pre-distorterprovided for compensating for non-linearity of the power amplifier.

In Step S22, the pre-distorted output signal from the pre-distorter isforwarded to the power amplifier.

In Step S23, Parameters of the pre-distorter are adapted based on anerror between the linearized signal output from the power amplifier andthe signal to be amplified using an adaptive direct learning algorithm.

In step S24, the linear system of equations formed by the directlearning algorithm are solved using a conjugate gradient algorithm,wherein, once per direct learning algorithm adaptation, at least one ofthe initial residual and the initial direction of the conjugate gradientalgorithm are set based on the result of the previous adaptation.

FIG. 3 shows a principle configuration of an example for an apparatusaccording to certain embodiments of the present invention, which isconfigured to implement stabilization of the direct learning algorithmfor wideband signals described In connection with some of the exampleversions of the disclosure. It is to be noted that the apparatus maycomprise elements or functions, such as a chipset, a chip, a moduleetc., which can also be part of a (network) element or attached as aseparate element to a (network) element, or the like. It should beunderstood that each block and any combination thereof may beimplemented by various means or their combinations, such as hardware,software, firmware, one or more processors and/or circuitry.

The apparatus 30 shown in FIG. 3 may comprise a processing function,control unit or processor 31, such as a CPU or the like, which issuitable for executing instructions given by programs or the likerelated to the network element control procedure.

The processor 31 is configured to execute processing related to theabove described stabilization of the direct learning algorithm forwideband signals. In particular, the processor 31 comprises asub-portion 310 as an inputting unit configured to input a signal to beamplified to a pre-distorter provided for compensating for non-linearityof the power amplifier. The portion 310 may be configured to performprocessing according to S21 of FIG. 2. Furthermore, the processor 31comprises a sub-portion 311 usable as a forwarding unit configured toforward the pre-distorted output signal from the pre-distorter to thepower amplifier. The portion 311 may be configured to perform processingaccording to S22 of FIG. 2. Furthermore, the processor 31 comprises asub-portion 312 usable as a adaptation unit configured to adaptparameters of the pre-distorter based on an error between the linearizedsignal output from the power amplifier and the signal to be amplifiedusing an adaptive direct learning algorithm. The portion 312 may beconfigured to perform processing according to S23 of FIG. 2.Furthermore, the processor 31 comprises a sub-portion 313 usable as asolving unit configured to solve the linear system of equations formedby the direct learning algorithm using a conjugate gradient algorithm,wherein, once per direct learning algorithm adaptation, at least one ofthe initial residual and the initial direction of the conjugate gradientalgorithm are set based on the result of the previous adaptation. Theportion 313 may be configured to perform processing according to S24 ofFIG. 2.

Reference signs 32 and 33 denote input/output (I/O) units (interfaces)connected to the processor 31. The I/O units 32 may be used forcommunicating with a (network) element. The I/O units 33 may be used forcommunicating with a management application. Reference sign 34 denotes amemory usable, for example, for storing data and programs to be executedby the processor 31 and/or as a working storage of the processor 31.

These measures enable to run the adaptive DLA algorithm perpetuallywithout an accumulated numerical error, with a significant reduction inconjugate gradient steps, and achieving guaranteed convergence withproper initialization.

According to certain embodiments of the present invention, both the DLAalgorithm as well as the conjugate gradient steps are modified.

That is, a modified of DLA algorithm according to certain embodiments isshown below in equations (11) and (12):

At adaptive step n:

X=[x′(n)x′(n−1)x′(n−T) . . . x′(n)|x(n)|^(L1) x′(n−1)|x′(n−1)|^(L1)x′(n−T)|x′(n−T)|x′(n−T)|^(L1)

x′(N+n)x′(N+n−1)x′(N+n−T) . . . x′(N+n)|x′(N+n)|^(L1)x′(N+n−1)|x′(N+n−1)|^(L1) x′(N+n−T)|x′(N+n−T)|^(L1)]

H=[h′(n)h′(n−1) . . . h′(n−T)]^(T)

(X ^(H) X)*H=X ^(H) E

E=[e′(n)e′(n+1) . . . e′(n+N)]^(T)

A*H=b form  (12)

x is a matrix that consists of linear and non-linear elements. In theA*H=b form, A is the autocorrelation matrix (X^(H) X) and the b is thecross correlated vector X^(H)E. L1 in the above equation depicts theorder of non-linearity. It is to be noted that in this terminology e(n)is a vector at n^(th) time, where as e′(n) is not. Similarly h′(n) isnot a vector but a single sample. H is a vector.

The generation of the pre-distorted signal at the adaptive step n isperformed according to the following equations (13) and (14):

y(n)=x(n)−μ*e(n)[Modified DLA step]  (13)

where, e(n)=X*H  (14)

The main modification to the adaptive DLA algorithm according to certainembodiments of the invention is the introduction of the error scalingfactor μ. The Error scaling factor of the normal DLA algorithm is equalto 1.0. However, the modified adaptive DLA algorithm according tocertain embodiments of the invention provides error scaling factors thatare smaller than 1.0 (i.e. μ=0.1, 0.2, 0.25, 0.5 . . . ).

A smaller error scaling factor achieves less numerical erroraccumulation and a much more close approximation of the actual globalminima. This, however, does not fully eliminate instability. Instabilitymay still occur at much later adaptations.

While the amount of numerical error accumulation is less with a smallerp, modifications to conjugate gradient steps provides complete stabilityof the adaptive DLA algorithm. Hence, according to certain embodimentsof the present invention, Improved conjugate gradient steps for AdaptiveDLA are provided as follows.

As discussed above, the conjugate gradient technique will be used tosolve the linear system of equations A*H=b formed by the adaptive DLADPD algorithm.

At the Initial step r₀ (the residual) and the direction d₀ are assignedto be equal to the cross correlation matrix. This step also assumes thatx₀=[0, 0, 0, . . . 0] (the solution is assumed to be a vector of zeros).Better initial conditions may exist and are discussed later.

In the following equations (15) to (17) the DLA adaptation number isdepicted with letter n.

At n=0 [The very first DLA adaptation]

d _(n) =r _(n) =b [with initial conditions stated above]  (15)

At n>0 [At n^(th) DLA adaptation] (Note that DLA adaptation never stops)

r _(init) =b−A*x _(n−1)  (16)

[wherein x_(n−1) is the solution at the (n−1)^(th) DLA adaptation]

d _(init) =r _(init)  (17)

The above two steps are performed only once per ever DLA adaptation. Itsets the initial residual and initial direction at the beginning of then^(th) adaptation.

One of the important functions of this initial residual equation is toeliminate the accumulated numerical error. On the other hand, settingthe initial direction helps restore the orthorgonality of the residual.Residual orthorgonality can be degraded due to numerical erroraccumulation. As stated, the frequency of this step is independent ofthe size of the matrix A and need to be performed only at the beginningonly of the DPD DLA adaptation.

In addition, r_(init) is computed with the partially converged previoussolution x_(n−1). Hence, the use of previous result eliminates thenecessity of large iterative steps of required of the conjugate gradienttechnique (see below).

Loop1 of the conjugate gradient Step (using r_(init) and d_(init))

$\begin{matrix}{\alpha_{1} = \frac{r_{init}^{T}r_{init}}{d_{init}^{T}A\; d_{init}}} & (18)\end{matrix}$

wherein α₁ is a constant

x ₁ =x _(n−1)+α₁ d ₁  (19)

wherein x_(n−1) is the previously converged solution in adaptation n

$\begin{matrix}{r_{1} = {r_{init} - {\alpha_{1}{Ad}_{init}}}} & (20) \\{\beta_{1} = \frac{r_{1}^{T}r_{1}}{r_{init}^{T}r_{init}}} & (21)\end{matrix}$

wherein β₁ is a constant

d ₁ =r ₁+β₁ d _(init)  (22)

End of loop 1

Repeating this loop from k=2 to Imax (Typical Imax values are 4, 12, . .. 32):

$\begin{matrix}{\alpha_{k} = \frac{r_{k}^{T}r_{k}}{d_{k}^{T}{Ad}_{k}}} & (23)\end{matrix}$

wherein α_(k) is a constant

x _(k) =x _(k−1)+α_(k) d _(k)  (24)

wherein x_(k) is the current approximation to the vector H in (A*H=b)

r _(k) =r _(k−1)−α_(k) Ad _(k)  (25)

wherein r_(k) is the new residual

$\begin{matrix}{\beta_{k} = \frac{r_{k}^{T}r_{k}}{r_{k - 1}^{T}r_{k - 1}}} & (26)\end{matrix}$

wherein β_(k) is a constant

d _(k) =r _(k)+β_(k) d _(k−1)  (27)

wherein d_(k) is the new direction

End of loop when k=Imax

As shown above, the improved conjugate gradient algorithm will onlyiterate up to Imax. Generally, at the first few adaptations, Imax can beas high as 32. Later, it can be reduced to something as small as 4 ifadequate convergence is needed. This achieves a significant reduction ofconjugate gradient steps. It does not, however, sacrifice any accuracyof the solution x_(k). This is because the improved conjugate gradientalgorithm does not waste the partially converged results from previousadaptations. Instead, it uses previous results to as a benefit.

The advantages of the embodiments of the present invention providereduced use of the ASIC resources and improved performance compared tothe existing fixed point based iterative inversion method. Due to theiterative nature of the improved DLA method, it is also ideally suitedfor small cells.

In the foregoing exemplary description of the apparatus, only the unitsthat are relevant for understanding the principles of the invention havebeen described using functional blocks. The apparatuses may comprisefurther units that are necessary for its respective function. However, adescription of these units is omitted in this specification. Thearrangement of the functional blocks of the apparatuses is not construedto limit the invention, and the functions may be performed by one blockor further split into sub-blocks.

According to exemplarily embodiments of the present invention, a systemmay comprise any conceivable combination of the thus depicteddevices/apparatuses and other network elements, which are arranged tocooperate as described above.

Embodiments of the present invention may be implemented as circuitry, insoftware, hardware, application logic or a combination of software,hardware and application logic.

As used in this application, the term “circuitry” refers to all of thefollowing: (a) hardware-only circuit implementations (such asimplementations in only analog and/or digital circuitry) and (b) tocombinations of circuits and software (and/or firmware), such as (asapplicable): (i) to a combination of processor(s) or (ii) to portions ofprocessor(s)/software (including digital signal processor(s)), software,and memory(ies) that work together to cause an apparatus, such as amobile phone or server, to perform various functions) and (c) tocircuits, such as a microprocessor(s) or a portion of amicroprocessor(s), that require software or firmware for operation, evenif the software or firmware is not physically present. This definitionof ‘circuitry’ applies to all uses of this term in this application,including in any claims. As a further example, as used in thisapplication, the term “circuitry” would also cover an implementation ofmerely a processor (or multiple processors) or portion of a processorand its (or their) accompanying software and/or firmware. The term“circuitry” would also cover, for example and if applicable to theparticular claim element, a baseband integrated circuit or applicationsprocessor integrated circuit for a mobile phone or a similar integratedcircuit in server, a cellular network device, or other network device.

The present invention relates in particular but without limitation tomobile communications, for example to environments under GSM, HSDPA,UMTS, LTE, WCDMA, WIMAX and WLAN and can advantageously be implementedalso in controllers, base stations, user equipments or smart phones, orpersonal computers connectable to such networks. That is, it can beimplemented as/in chipsets to connected devices, and/or modems thereof.

If desired, the different functions discussed herein may be performed ina different order and/or concurrently with each other. Furthermore, ifdesired, one or more of the above-described functions may be optional ormay be combined.

Although various aspects of the invention are set out in the independentclaims, other aspects of the invention comprise other combinations offeatures from the described embodiments and/or the dependent claims withthe features of the independent claims, and not solely the combinationsexplicitly set out in the claims.

It is also noted herein that while the above describes exampleembodiments of the invention, these descriptions should not be viewed ina limiting sense. Rather, there are several variations and modificationswhich may be made without departing from the scope of the presentinvention as defined in the appended claims.

The following meanings for the abbreviations used in this specificationapply:

3GPP 3^(rd) Generation Partnership Project DLA direct learning algorithmDPD Digital Pre-Distortion ILA Indirect Learning Algorithm IM InterModulation PA Power Amplifier RF Radio Frequency

1. A method, comprising: inputting a signal to be amplified to apre-distorter provided for compensating for non-linearity of a poweramplifier; forwarding the pre-distorted output signal from thepre-distorter to the power amplifier; adapting parameters of thepre-distorter based on an error between a linearized signal output fromthe power amplifier and the signal to be amplified using an adaptivedirect learning algorithm; and solving a linear system of equationsformed by the adaptive direct learning algorithm using a conjugategradient algorithm, the solving comprising, once per adaptation of theadaptive direct learning algorithm, setting at least one of an initialresidual and an initial direction of the conjugate gradient algorithmbased on a result of a previous adaptation.
 2. The method according toclaim 1, wherein the initial residual and/or the initial direction ofthe conjugate gradient algorithm is/are set at a beginning of theadaptation.
 3. The method according to claim 1, wherein the initialresidual and/or the initial direction of the conjugate gradientalgorithm is/are set so as to fulfill the following equations:r _(init) =b−A*x _(n−1)d _(init) =r _(init) wherein r_(init), is an initial residual vector forthe initial residual, d_(init), is an initial direction vector for theinitial direction, b is a cross-correlated vector of the error, A is anautocorrelation matrix, and x_(n−1) is a solution vector at the(n−1)^(th) adaptation of the direct learning algorithm.
 4. The methodaccording to claim 1, wherein loops of the conjugant gradient algorithmare iterated until reaching a preset number of loops.
 5. The methodaccording to claim 1, wherein the initial residual and/or the initialdirection of the conjugate gradient algorithm is/are computed based on apartially converged solution of the previous adaptation.
 6. The methodaccording to claim 1, wherein an error scaling factor is introduced inthe adaptive direct learning algorithm, so as to fulfill the followingequation:y(n)=x(n)−μ*e(n) wherein y is the pre-distorted signal vectorcorresponding to the pre-distorted output signal, x is a vector of thesignal to be amplified, e is an error vector corresponding to the error,μ is the error scaling factor, and n indicates an adaptation number fora current adaptation.
 7. The method according to claim 6, wherein theerror scaling factor is set to a value smaller than 1.0.
 8. Anapparatus, comprising: a pre-distorter; a power amplifier; at least oneprocessor, and at least one memory for storing instructions to beexecuted by the processor, wherein the at least one memory and theinstructions are configured to, with the at least one processor, causethe apparatus at least to perform inputting a signal to be amplified toa pre-distorter provided for compensating for non-linearity of the poweramplifier; forwarding the pre-distorted output signal from thepre-distorter to the power amplifier; adapting parameters of thepre-distorter based on an error between a linearized signal output fromthe power amplifier and the signal to be amplified using an adaptivedirect learning algorithm; and solving a linear system of equationsformed by the adaptive direct learning algorithm using a conjugategradient algorithm, the solving comprising, once per adaptation of thedirect learning algorithm, setting at least one of the initial residualand the initial direction of the conjugate gradient algorithm based on aresult of a previous adaptation.
 9. The apparatus according to claim 8,wherein the initial residual and/or the initial direction of theconjugate gradient algorithm is/are set at a beginning of an adaptation.10. The apparatus according to claim 8, wherein the initial residualand/or the initial direction of the conjugate gradient algorithm is/areset so as to fulfill the following equations:r _(init) =b−A*x _(n−1)d _(init) =r _(init) wherein r_(init), is an initial residual vector forthe initial residual, d_(init), is an initial direction vector for theinitial direction, b is a cross-correlated vector of the error, A is andautocorrelation matrix, and x_(n−1) is a solution vector at an(n−1)^(th) adaptation of the direct learning algorithm.
 11. Theapparatus according to claim 8, wherein loops of the conjugant gradientalgorithm are iterated until reaching a preset number of loops.
 12. Theapparatus according to claim 8, wherein the initial residual and/or theinitial direction of the conjugate gradient algorithm is/are computedbased on a partially converged solution of the previous adaptation. 13.The apparatus according to claim 8, wherein an error scaling factor isintroduced in the adaptive direct learning algorithm, so as to fulfillthe following equation:y(n)=x(n)−μ*e(n) wherein y is a pre-distorted signal vectorcorresponding to the pre-distorted output signal, x is a vector of thesignal to be amplified, e is an error vector corresponding to the error,μ is the error scaling factor, and n indicates an adaptation number fora current adaptation.
 14. The apparatus according to claim 13, whereinthe error scaling factor is set to a value smaller than 1.0.
 15. Acomputer program product for a computer, comprising a non-transitorycomputer-readable medium having software code portions thereon forcausing the computer to perform the steps of claim 1 when said productis run on the computer.
 16. (canceled)
 17. The method according to claim1, wherein setting comprises setting both the initial residual and theinitial direction of the conjugate gradient algorithm based on theresult of the previous adaptation, and, for a very first adaptation,setting the initial residual and the initial direction of the conjugategradient algorithm based on a cross-correlated vector of the error, thecross-correlated vector used in the linear system of equations, andwherein, for adaptations after the very first adaptation, setting boththe initial residual and the initial direction of the conjugate gradientalgorithm based on the result of the previous adaptation.